1. Field of the Invention
The teachings generally relate to a non-mechanistic, differential-equation-free approach for predicting a particular response of a system to a given input.
2. Description of the Related Art
Research and development has historically relied on physical modeling to develop new technologies. Given the speed at which computers can perform computations, and the vast amount of computer memory available, computer modeling allows us to speed-up and reduce costs of research by facilitating the creation of a large number of simulations over a wide range of physical scales very quickly. As with physical modeling, computer modeling and simulation deals with first characterizing and then predicting input-response type relationships. What type of reaction will occur between two chemicals? What is the flow response when a given amount of water is introduced into a particular porous media? How will the components of a watershed—rivers, reservoirs, aquifers, etc.—react when subjected to a given rainfall or contamination event? How will a person's blood glucose level respond to a given meal? How will a diseased tissue respond to a drug regimen? These are all input-response-type questions that can be addressed through mathematical/computational modeling and simulation. Generally speaking, this can be referred to as “input-response modeling”. In the field of drug design, this can also be referred to as “dose-response modeling.” An accurate model will give researchers a way of running simulations to quickly observe and test a large number of complex input-response phenomena that might be too costly and time-consuming to observe and test in a real-world setting.
The reliance on physical modeling can be very expensive, which makes the use of computer modeling an attractive way to reduce costs. For example, the average drug developed by a major pharmaceutical company costs at least $4 billion, and it can be as much as $11 billion. The range of money spent is quite wide, for example, as AstraZeneca has spent about $12 billion in research money for every new drug approved; Eli Lilly spent about $4.5 billion per drug; and, Amgen has spent about $3.7 billion per drug. The costs are so high, at least in part, because single clinical trial can cost $100 million, and the combined cost of manufacturing and clinical testing for some drugs can add up to $1 billion. Computer modeling of drugs, if improved such that it can be done efficiently and effectively, can cut costs and help make the business of drug discovery more attractive. Other industries, of course, can also benefit from such efficient and effective computer modeling methods.
State-of-the-art systems and methods, however, typically use mechanistic computer models to try and avoid the costs of physical modeling. Unfortunately, such models can be very complex, insufficient and ambiguous, and moreover, lacking in accuracy. Such models use established empirical formulas as “first principles” that provide the framework to make “mechanistic” predictions. Complex biological systems can be modeled, for example, using laboratory experiments to establish such first-principle-type relationships between components of the system. For example, laboratory experiments can be used to determine the ways in which a certain disease progresses in the human body, and this can be used to help predict how effective a drug might be in stopping, or slowing down, the progression of a disease.
Unfortunately, the current, state-of-the-art approaches have some serious limitations. There are problems, for example, in dealing with heterogeneous and complex systems, in that the models fail by insufficiently characterizing the systems. Predicting the flow of rainfall through the ground to an adjacent stream, for example, involves a complex and heterogeneous combination of media types in the ground. The variations throughout the media make it difficult-to-impossible to apply Darcy's Law accurately in such a complex system. And, although possible in theory, accurately identifying and modeling such complex and heterogeneous media throughout the system is often considered cost prohibitive, as well as time prohibitive in many cases. As the systems become more mechanistically complex, of course, we need more empirical relationships and a more complex model. Hydraulic conductivity mechanisms may not be enough, for example, as there can also be chemical reaction mechanisms affecting the movement of the fluids. Human biological systems are examples of highly complex systems that are difficult to scale from the lab to the human body, as measurements that can be taken in the lab may not be obtainable in the human body, for example. In predicting the response of a tumor to a drug, for example, measuring in vitro or ex vivo tumor size and growth in small time scales is one thing, but getting such in vivo measurements can be difficult-to-impossible. In addition, a system may have nonlinearities that need to be addressed, requiring further and often futile attempts at adjusting the mechanistic model. Moreover, current models often cannot map input properties to model parameters. This is because they lack the necessary one-to-one relationships between model parameters and model output. This lack of specificity results in an ambiguity between model parameters and output that makes it impossible to get unique input-response relationships, such that the same input can produce a wide range of responses, or many different inputs could produce the same response.
Accordingly, one of skill will appreciate a data-based, non-mechanistic, differential-equation-free approach for predicting a particular response of a system to a given input. In particular, one of skill will appreciate having the ability to (i) reduce the cost of research and development by offering an accurate modeling of heterogeneous and complex physical systems; (ii) reduce the cost of creating such systems and methods by simplifying the modeling process; (iii) accurately capture and model inherent nonlinearities in cases where sufficient knowledge does not exist to a priori build a model and its parameters; and, (iv) provide one-to-one relationships between model parameters and model outputs, addressing the problem of the ambiguities inherent in the current, state-of-the-art systems and methods.